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Mathematics > Numerical Analysis

arXiv:1611.01420 (math)
[Submitted on 4 Nov 2016 (v1), last revised 21 Jan 2018 (this version, v3)]

Title:An integral equation-based numerical solver for Taylor states in toroidal geometries

Authors:Michael O'Neil, Antoine J. Cerfon
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Abstract:We develop an algorithm for the numerical calculation of Taylor states in toroidal and toroidal shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter $\lambda$ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph); Plasma Physics (physics.plasm-ph)
Cite as: arXiv:1611.01420 [math.NA]
  (or arXiv:1611.01420v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1611.01420

Submission history

From: Michael O'Neil [view email]
[v1] Fri, 4 Nov 2016 15:23:42 UTC (2,353 KB)
[v2] Thu, 3 Aug 2017 04:23:54 UTC (2,356 KB)
[v3] Sun, 21 Jan 2018 17:53:06 UTC (2,357 KB)
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